A Treatise on Plane and Spherical Trigonometry: Including the Construction of the Auxiliary Tables ; a Concise Tract on the Conic Sections, and the Principles of Spherical Projection |
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Page 37
... perpendicular , so is radius to the sine of the angle at the base ; as the hypothenuse is to the base , so is radius to the cosine of the angle at the base ; and as the base is to the perpendicular , so is radius to the tangent of the ...
... perpendicular , so is radius to the sine of the angle at the base ; as the hypothenuse is to the base , so is radius to the cosine of the angle at the base ; and as the base is to the perpendicular , so is radius to the tangent of the ...
Page 41
... perpendicular falling upon it from the vertex of the triangle . F B A H D F G Let ABC be a trian- gle , whose base is AB . From the vertex C , with the greater side AC , de- scribe the circle AEGF , cutting BC produced in E and F , and ...
... perpendicular falling upon it from the vertex of the triangle . F B A H D F G Let ABC be a trian- gle , whose base is AB . From the vertex C , with the greater side AC , de- scribe the circle AEGF , cutting BC produced in E and F , and ...
Page 66
... perpendicular , describe a circle passing through A , and cutting FEG in G ; join GD , and produce it to cut the circle in C ; join CA , CB ; and ACB will be the triangle required . = Since AE = BE , and the angles at E are right ones ...
... perpendicular , describe a circle passing through A , and cutting FEG in G ; join GD , and produce it to cut the circle in C ; join CA , CB ; and ACB will be the triangle required . = Since AE = BE , and the angles at E are right ones ...
Page 73
... perpendicular DE = radius of the inscribed circle 12 ; from E , with the dis- tance ED , describe a circle ; through A and B draw the lines AH , BH , touching the circle in F and G ; ABH is the triangle required . = Join EF , EG ; then ...
... perpendicular DE = radius of the inscribed circle 12 ; from E , with the dis- tance ED , describe a circle ; through A and B draw the lines AH , BH , touching the circle in F and G ; ABH is the triangle required . = Join EF , EG ; then ...
Page 74
... perpendicular BC = radius of the inscribed circle 10 ; through C , draw CG parallel to AB ; make the angle BCD = comple- ment of half the vertical angle , 55 ° ; bisect AD in E ; draw EF at right angles to AD , meeting CD produced in F ...
... perpendicular BC = radius of the inscribed circle 10 ; through C , draw CG parallel to AB ; make the angle BCD = comple- ment of half the vertical angle , 55 ° ; bisect AD in E ; draw EF at right angles to AD , meeting CD produced in F ...
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Common terms and phrases
ABDP adjacent angle angled spherical triangle base bisect C.cos c.sin centre circle Art common section Comp AC cone conical surface consequently construction cosec cosine cotan directrix distance EB² EC² ecliptic ED² ellipse equal equation given angle greater axis Hence hyperbola hypothenuse join latus rectum less circle Let ABC line of measures logarithms meet opposite ordinate original circle parabola parallel perpendicular plane of projection primitive circle projected circle projected pole projecting point Q. E. D. ART Q. E. D. Cor quadrant radius right angled spherical right ascension right line secant semicircle semitangent sides similar triangles sine sphere spherical angle tangent tangent of half touches the circle triangle ABC vertex vertical angle whence wherefore